Python Scripting: (relative) Locations and Rotations of Objects under Empty
Search for answers, use the python console

The piece of advice I'd impart for those keen on learning python via blender, is to get your hands dirty and "nut these things out" yourself

Here is python console code. Firstly get all the empties in the scene objects collection via a list comprehension.  C is context.

&gt;&gt;&gt; empties = [e for e in C.scene.objects if e.data is None]


Then loop thru the child objects of each of empties.  Writes the object's name, its location and euler rotation from the basis matrix and directly from the properties.

For global use ob.matrix_world

&gt;&gt;&gt; for e in empties:
...     for o in e.children:
...         o.name
...         o.matrix_basis.to_translation()
...         o.location
...         o.matrix_basis.to_euler()
...         o.rotation_euler
...         


Output

'Icosphere'
Vector((0.08762237429618835, -0.26966890692710876, -0.9004361629486084))
Vector((0.08762237429618835, -0.26966890692710876, -0.9004361629486084))
Euler((2.8039052486419678, 7.291294679134808e-08, 0.31416523456573486), 'XYZ')
Euler((2.8039052486419678, 7.291294679134808e-08, 0.31416523456573486), 'XYZ')
'Icosphere.001'
Vector((0.47059956192970276, -0.5479161143302917, -0.6078704595565796))
Vector((0.47059956192970276, -0.5479161143302917, -0.6078704595565796))
Euler((2.2938785552978516, -1.0633498526146923e-08, 0.679742157459259), 'XYZ')
Euler((2.2938785552978516, -1.0633498526146923e-08, 0.679742157459259), 'XYZ')
'Icosphere.002'
Vector((-0.05865825340151787, -0.7198853492736816, -0.6078706383705139))
Vector((-0.05865825340151787, -0.7198853492736816, -0.6078706383705139))
Euler((2.2938790321350098, -1.5278347476055387e-08, -0.051412295550107956), 'XYZ')
Euler((2.2938790321350098, -1.5278347476055387e-08, -0.051412295550107956), 'XYZ')